The goal of this paper is to present, from the $b$-calculus perspective, a program for analyzing generalized resolvent families and heat kernels of pseudodifferential operators on conic manifolds. To carry this out, a new class of parameter-dependent cone pseudodifferential operators is developed and studied.
"Parameter-dependent operators and resolvent expansions on conic manifolds." Illinois J. Math. 46 (4) 1035 - 1059, Winter 2002. https://doi.org/10.1215/ijm/1258138464